Strongly exposed points in Lebesgue-Bochner function spaces

Abstract

It is a result of Peter Greim that if f f is a strongly exposed point of the unit ball of Lebesgue-Bochner function space L p ( μ , X ) , 1 > p > ∞ {L^p}(\mu ,X),\;1 > p > \infty , then f f is a unit vector and f ( t ) / | | f ( t ) | | f(t)/||f(t)|| is a strongly exposed point of the unit ball of X X for almost all t t in the support of f f . We prove that the converse is also true.